Coordinates and trigonometry · Ages 12–13

Rotation about the origin worksheet

Part of: First steps in coordinates

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Coordinates and trigonometry · Ages 12–13

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.(6, −4) turned 180° about the origin goes to (, ).
Fill in each blank
Answer:
2.(−6, −7) turned 90° anticlockwise about the origin goes to (, ).
Fill in each blank
Answer:
3.(6, −4) turned 90° anticlockwise about the origin goes to (, ).
Fill in each blank
Answer:
4.(4, −4) turned 90° clockwise about the origin goes to (, ).
Fill in each blank
Answer:
5.Turned 90° anticlockwise about the origin, (−1, 8) lands in quadrant .
Answer:
6.(−4, 8) turned 90° clockwise about the origin goes to (, ).
Fill in each blank
Answer:
7.Turned 90° anticlockwise about the origin, (5, 1) lands in quadrant .
Answer:
8.(9, −9) turned 270° anticlockwise about the origin goes to (, ).
Fill in each blank
Answer:

13.A(1, 6) is turned 90° clockwise about the origin to B, and B reflected in the y-axis to C. B is (, ) and C is (, ).
Fill in each blank
Working:
Answer:
14.A(−3, −5) is turned 90° anticlockwise about the origin to B, then B is translated 6 units right to C. What are C's coordinates?
- A. (−1, −3)
- B. (11, −3)
- C. (5, 503)
- D. (1, 3)
Choose the right answer
Working:
Answer:
15.A(1, −1) turned 180° about the origin is B. A rectangle has AB as a diagonal and sides parallel to the axes. What is its area, in square units?
Working:
Answer:
16.Triangle ABC is turned 180° about the origin to A′B′C′. With A(−3, 4) and B(−5, −6), A′ is (, ) and B′ is (, ).
Fill in each blank
Working:
Answer:
17.B is the image of A turned 180° about the origin, and B is (2, −1). What is A's x-coordinate?
Working:
Answer:
18.P turned 90° clockwise about the origin is Q(−1, 4). What are P's coordinates?
- A. (399, −1)
- B. (1, −4)
- C. (−4, −1)
- D. (401, 1)
Choose the right answer
Working:
Answer:

Show the answers and working

Rotation about the origin worksheet: Answers and working

1. −6, 4
A 180° turn takes it to the other side of the origin: both signs change, (−6, 4).
2. 7, −6
90° anticlockwise: (x, y) goes to (−y, x). Swap them, then change the sign of the new x: (7, −6).
3. 4, 6
90° anticlockwise: (x, y) goes to (−y, x). Swap them, then change the sign of the new x: (4, 6).
4. −4, −4
90° clockwise: (x, y) goes to (y, −x). Swap them, then change the sign of the new y: (−4, −4).
5. 3
The image is (−8, −1); its signs give quadrant 3. A quarter turn anticlockwise moves on one quadrant.
6. 8, 4
90° clockwise: (x, y) goes to (y, −x). Swap them, then change the sign of the new y: (8, 4).
7. 2
The image is (−1, 5); its signs give quadrant 2. A quarter turn anticlockwise moves on one quadrant.
8. −9, −9
270° anticlockwise is 90° clockwise: (x, y) → (y, −x), giving (−9, −9). Or turn 90° anticlockwise three times.

9. D. (1, 4)
90° clockwise: (x, y) → (y, −x), that is (1, 4). Check: it moves on one quadrant, clockwise.
10. B
90° anticlockwise: every corner (x, y) goes to (−y, x). A(−4, −3), for one, goes to A′(3, −4).
11. C. (2, −3)
90° clockwise: (x, y) → (y, −x), that is (2, −3). Check: it moves on one quadrant, clockwise.
12. A. 90° clockwise
The three turns give: 90° clockwise (−3, 6), 90° anticlockwise (3, −6), 180° (6, 3). The one matching (−3, 6) is the answer.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 6, −1, −6, −1
90° clockwise: (x, y) → (y, −x), B(6, −1); in the y-axis x changes sign: C(−6, −1).
14. B. (11, −3)
90° anticlockwise: B(5, −3); 6 right: C(11, −3).
15. 4
B is (−1, 1). The rectangle is as wide as the gap in x, 2, and as tall as the gap in y, 2: 2 × 2 = 4.
16. 3, −4, 5, 6
A 180° turn changes both signs at every corner: A′(3, −4), B′(5, 6).
17. −2
Another 180° brings it back to A: A is (−2, 1), with x = −2.
18. C. (−4, −1)
Undo it: turn Q 90° anticlockwise, (x, y) → (−y, x): P(−4, −1). Check: (−4, −1) turned 90° clockwise is (−1, 4).

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